There is a circle of a radius √(8/3).
There are 3 ellipses inside the circle which are tangent to the circle at points A, B, C and to each other at points D, E, F. Their major axes are parallel to lines tangent to the circle at corresponding tangency points. The lengths of major axes of the ellipses are 2√(3/2), 2√(8/7) and 2.
What is the ratio of the area of triangle ABC to the area of triangle DEF?